Short definition
A drying, puckering sensation in the mouth caused by tannins binding to proteins in your saliva.
That sandpapery feeling after sipping a young Cabernet Sauvignon? That is astringency. It is the same drying sensation you get from over-steeped black tea or biting an unripe persimmon. Some astringency adds structure, but too much makes wine harsh. Food with fat and protein — steak, aged cheese — softens it dramatically.